So, x cannot be equal to -3 or 4, because there, you have an asymptote.

At x = -4 and 2, you have f(x) = 0.

Anything negative is imaginary.

When you take the intervals, you have -4, -3, 2, 4.

And trying in values smaller than -4 gives a solution.

At -4, you have 0.

Between -4 and -3, you don't have any solution.

At -3, you get infinity.

Between -3 and 2, you get solutions.

At 2, you get 0 again.

Between 2 and 4 you get no solutions.

At 4, you get again infinity and beyond that, you get solutions.